engUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25332016-01-01411185428Threshold harvesting policy and delayed ratio-dependent functional response predator-prey modelRazie Shafeii Lashkarianrazie_sh@yahoo.com1Dariush Behmardi Sharifabadbehmardi@alzahra.ac.ir2Department of Mathematics, University of Alzahra, Tehran, IranDepartment of Mathematics, Alzahra University, Tehran, IranThis paper deals with a delayed ratio-dependent functional response predator-prey model with a threshold harvesting policy. We study the equilibria of the system before and after the threshold. We show that the threshold harvesting can improve the undesirable behavior such as nonexistence of interior equilibria. The global analysis of the model as well as boundedness and permanence properties are examined too. Then we analyze the effect of time delay on the stabilization of the equilibria, i.e., we study whether time delay could change the stability of a co-existence point from an unstable mood to a stable one. The systemundergoes a Hopf bifurcation when it passes a critical time delay. Finally, some numerical simulations are performed tosupport our analytic results.http://cmde.tabrizu.ac.ir/article_5428_fa1f77b2c0cba4797f160a0a7a448e19.pdfPredator-prey modelratio-dependent functional responsethreshold harvestingtime delayHopf bifurcationengUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25332016-01-014119295429Existence of positive solution to a class of boundary value problems of fractional differential equationsAmjad Aliamjadalimna@yahoo.com1Kamal Shahkamalshah408@gmail.com2Rahmat Khanrahmat_alipk@yahoo.com3University of MalakandUniversity of MalakandDepartment of Mathematics University of MalakandThis paper is devoted to the study of establishing sufficient conditions forexistence and uniqueness of positive solution to a class ofnon-linear problems of fractional differential equations. The boundary conditionsinvolved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ containfractional order derivative which produce extra complexity. Thank to classical fixed point theorems of nonlinear alternative of Leray-Schauder and Banach Contraction principle, sufficient conditions are developed under which the proposed problem has at least one solution. An example has been provided to illustrate themain results.http://cmde.tabrizu.ac.ir/article_5429_e4b51aaaf607a9dc32a0613553911566.pdfBoundary value problemExistence and uniqueness resultsFractional differential differential equationsClassical fixed point theoremengUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25332016-01-014130425441An approach based on statistical spline model for Volterra-Fredholm integral equationsAmir Hossein Salehi Shayeganah.salehi@mail.kntu.ac.ir1Ali Zakeriazakeri@kntu.ac.ir2M. R. &lrm;Peyghamipeyghami@kntu.ac.ir3K. &lrm;N&lrm;. &lrm;Toosi University of TechnologyK. N. Toosi University of Technology&lrm;K&lrm;. &lrm;N&lrm;. &lrm;Toosi University of Technology‎In this paper‎, ‎an approach based on statistical spline model (SSM) and collocation method is proposed to solve Volterra-Fredholm integral equations‎. ‎The set of collocation nodes is chosen so that the points yield minimal error in the nodal polynomials‎. ‎Under some standard assumptions‎, ‎we establish the convergence property of this approach‎. ‎Numerical results on some problems are given to describe the introduced method‎. ‎A comparison between the numerical results and those obtained from Lagrange and Taylor collocation methods demonstrates that the proposed method generates an approximate solution with minimal error.http://cmde.tabrizu.ac.ir/article_5441_a9657fe62ac81db659aa73c9a11cdc0f.pdf‎Statistical spline modelVolterra-Fredholm integral equationsConvergence analysisengUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25332016-01-014143535442The comparison of optimal homotopy asymptotic method and homotopy perturbation method to solve Fisher equationzainab ayatiayati.zainab@gmail.com1sima ahmadysima.ahmadikia@gmail.com2Department of Engineering sciences, Faculty of Technology and Engineering East of Guilan, University of Guilan P.C.44891-Rudsar-Vajargah,IranDepartment of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, IranIn recent years, numerous approaches have been applied for ﬁnding the solutions of functional equations. One of them is the optimal homotopy asymptotic method. In current paper, this method has been applied for obtaining the approximate solution of Fisher equation. The reliability of the method will be shown by solving some examples of various kinds and comparing the obtained outcomes with the results of homotopy Perturbation method.http://cmde.tabrizu.ac.ir/article_5442_1274a06c80df611c4fca84aea6dcd196.pdfOptimal Homotopy Asymptotic methodHomotopy Perturbation methodFisher equationengUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25332016-01-014154695443On the split-step method for the solution of nonlinear Schr"{o}dinger equation with the Riesz space fractional derivativeAkbar Mohebbia_mohebbi@kashanu.ac.ir1Department of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, Iran.The aim of this paper is to extend the split-step idea for the solution of fractional partial differential equations.We consider the multidimensional nonlinear Schr"{o}dinger equation with the Riesz space fractional derivative andpropose an efficient numerical algorithm to obtain it's approximate solutions. To this end, we first discretize the Riesz fractional derivative then apply the Crank-Nicolson and a split-step methods to obtain a numerical method for this equation. In the proposed method there is no need to solve the nonlinear system of algebraic equations and the method is convergent and unconditionally stable.The proposed method preserves the discrete mass which will be investigated numerically. Numerical results demonstrate the reliability, accuracyand efficiency of the proposed method.http://cmde.tabrizu.ac.ir/article_5443_cedd8d12d1c83ea1861e67cef8734362.pdfFinite difference methodRiesz space fractional derivativesUnconditional stabilitySchr"{o}dinger equationengUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25332016-01-014170985444Analytical solution of MHD flow and heat transfer over a permeable nonlinearly stretching sheet in a porous medium filled by a nanofluidAmir Parsaamirbparsa@yahoo.com1Habib-Olah Sayehvandhsayehvand@yahoo.com2Student of Mechanical Engineering, Mechanical Engineering Department, Engineering Faculty of Bu-Ali Sina University, Hamedan, IranAssistant Professor of Mechanical Engineering, Mechanical Engineering Department, Engineering Faculty of Bu-Ali Sina University, Hamedan, Iran. Email: hsayehvand@yahoo.comIn this paper, the differential transform method and Padé approximation (DTM-Padé) is applied to obtain the approximate analytical solutions of the MHD flow and heat transfer of a nanofluid over a nonlinearly stretching permeable sheet in porous. The similarity solution is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations which are then solved by DTM-Padé and validity of our solutions is verified by the numerical results (fourth-order Runge-Kutta scheme with the shooting method). The stretching velocity of sheet is assumed to have a power-law variation with the horizontal distance along the plate. It was shown that the differential transform method (DTM) solutions are only valid for small values of independent variable but the obtained results by the DTM-Padé are valid for the whole solution domain with high accuracy. Finally, the analytical solutions of the problem for different values of the fixed parameters are shown and discussed. Furthermore, it is found that permeability parameter of medium has a greater effect on the flow and heat transfer of a nanofluid than the magnetic parameter.http://cmde.tabrizu.ac.ir/article_5444_3b8dd28d47f63c309745589a4a13de10.pdfDTM-PadéMHDNanofluidPorous mediumPrescribed temperature